The baby is the Prince of Wales' first grandchild, and has already been sent best wishes from all over the world.

Congratulatory messages from Telegraph readers

Congratulations on the arrival of your new little man! In a cynical world where the news is usually distressing, it's been a breath of fresh air to follow your lives from your wedding to the birth of your new baby. You have transformed your country's monarchy and I look forward to what the future will bring to both of you and your growing family.

Advice: don't take parenting too seriously; never be afraid to say "because I told you so"; take time for yourselves; let Harry babysit now and again (every child deserves to have an aunt or uncle who's tons of fun); and enjoy every moment you can. They do grow up awfully quickly.

Elizabeth McKinley

Denver, Colorado, United States

Your Royal Highnesses:

Everyone here in my corner of the State of Michigan, United States wishes to congradulate you both on the safe delivery of your healthy baby son. Good job !!!

Barbara Sherwin,

Novi, Michigan, United States

With every good wish to the Duke and Duchess of Cambridge on the birth of the Prince of Cambridge. The nation is noticeably delighted at this time, as indeed am I. Wishing the royal couple and the baby very good health and a long, fulfilling life. Her Majesty must surely be truly delighted, as will be Prince Charles and Camilla.

Richard Lewis, Wales

We'd like to send our love and congratulations to the couple on the princes' birth from Southern Louisiana!

Best wishes on a bright future, and 'Laissez le bon temps rouler ya'll!' ('Let the good times roll y'all!)

Parrish Frisbee, Abita Springs, Louisiana, United States

From one mum to another I wanted to say a big well done to the Duchess on the safe arrival of her and the Duke's baby boy. I watched the news coverage with my 7 year old son last night and it bought back all those feelings I had when he was born. It is the most precious thing to bring life into the world. Congratulations to you both and your families. Treasure him and each other.

Nicky, Freddie and Alfie

Market Harborough

What a wonderful day! I wish I was in London to hear the bells peal at Westminster Abbey! I always have had the Royal Family as part of my family in a sense. I'm so glad that everything went well and the Duchess was delivered of a healthy baby boy. I hope the media scrutiny won't be too hard on them, or the baby growing up, and that they will receive the utmost respect and privacy from the world's press. It's a family time. On behalf of my whole family I send my love and best wishes from Canada.

Pamela Ewen,

Toronto, Canada

Congratulations. We are so thrilled for you both in welcoming you new baby son. Your lives will change forever and as each year goes by, he will bring you more joy and happiness as he grows into being his own person.

Health and happiness to your family.

Mark, Stacy, Keri and Daniel Lindow

Kent

My heartfelt congratulations to the Duke and Duchess of Cambridge on the birth of their bouncing baby boy!

I wish them all a long life of health and happiness.

God bless the future King!

Best regards,

Sarah Kliparchuk

Edmonton, Alberta, Canada

Dear new royal parents,

Congratulations on the birth of your new-born baby.

To you he will soon crawl, run, jump, cry and laugh.

To us, he represent a vision of all that is hopeful and new.

May he bring you all the joy in the world and we thank you that we may also share in the joy.

Lots of new-born regards from South Africa

Dayne Elizabeth Nel, Hermanus, South Africa

Your Royal Highnesses,

Congratulations on the birth of your first child! I understand that this is a private joy for you, but many of us are delighted by the news as well. I wish you all continued health and happiness. Long live the monarchy!

Yours faithfully,

Andrea Zuvich

Your Royal Highnesses,

A heartfelt congratulations from across the pond! What a privilege it is for us as Canadians to enjoy the benefits of our system of constitutional monarchy. Sir, it is your grandmother who serves as the bond between Britain and Canada, and someday your father, and then you, shall do the same. I am thrilled that my children shall enjoy the reign of your son in the future! May God bless you as parents (believe me, it isn't easy!) and may you raise your boy to be a humble servant to his people, and a source of inspiration to good for all who know him.

The birth of your son is a little extra fun for me as my 16th great grandfather was John Spencer, who is your 17th great grandfather.. That makes us 17th cousins once removed (I imagine this doesn't warrant an invitation to drop by when we're in town, but feel free to say you have family in Canada if you think that will help strengthen the ties...lol).

Again, a huge congratulations to the Royal family, the Middleton family and the Spencer family. May God richly bless you!